On Contact Numbers of Finite Lattice Sphere Packings and the Maximal Coordination of Monatomic Crystals

Abstract

We algorithmically characterize the maximal contact number problem for finite congruent lattice sphere packings in ${\mathbb{R}}^d$ and show that in ${\mathbb{R}}^3$ this problem is equivalent to determining the maximal coordination of a monatomic crystal.

6 pages, 1 figure

References in corpus (2)

• Deriving Finite Sphere Packings
• Regular Totally Separable Sphere Packings

Cited by in corpus (3)

• On Contact Numbers of Finite Lattice Sphere Packings of 20-27 Balls
• On the Contact Numbers of Ball Packings on Various Hexagonal Grids
• On Arrangements of Six, Seven, and Eight Spheres: Maximal Bonding of Monatomic Ionic Compounds